Wallace has a $500 budget for a pizza party. Pizza pies cost $12 each. He will also purchase drinks for $30, paper plates for $15 and napkins for $6. Write and solve an inequality that shows how many pizza pies Wallace can purchase.
12p + 30 + 15 + 6 < 500
12p < 500 - 51
p < 449/12
p < ?
37
Let's denote the number of pizza pies that Wallace can purchase as "x".
The cost of x pizza pies is given by 12x.
The total cost of the pizza pies, drinks, paper plates, and napkins should be less than or equal to Wallace's budget of $500:
12x + 30 + 15 + 6 ≤ 500
Combining like terms, we have:
12x + 51 ≤ 500
To isolate x, we subtract 51 from both sides:
12x ≤ 500 - 51
12x ≤ 449
Finally, we divide both sides by 12:
x ≤ 449/12
So, Wallace can purchase a maximum of 37 pizza pies.
To solve this problem, we need to first set up an inequality that represents the situation. Let's x be the number of pizza pies that Wallace can purchase within his budget.
The cost of x pizza pies can be expressed as 12x.
Adding the cost of drinks, paper plates, and napkins, we get the total cost of the party, which must be less than or equal to Wallace's budget of $500.
So, the inequality can be written as:
12x + 30 + 15 + 6 ≤ 500
Combining like terms, we have:
12x + 51 ≤ 500
Now, we can solve for x:
12x ≤ 500 - 51
12x ≤ 449
x ≤ 449/12
x ≤ 37.42
Since we cannot purchase a fraction of a pizza pie, we round down to the nearest whole number.
Therefore, Wallace can purchase a maximum of 37 pizza pies (x ≤ 37) within his budget.